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Are exposures associated with disease?

Epidemiology matters: a new introduction to methodological foundationsChapter 6

Epidemiology Matters – Chapter 1 2

Seven steps

1. Define the population of interest2. Conceptualize and create measures of exposures and health

indicators3. Take a sample of the population4. Estimate measures of association between exposures and health

indicators of interest5. Rigorously evaluate whether the association observed suggests a

causal association6. Assess the evidence for causes working together7. Assess the extent to which the result matters, is externally valid, to

other populations


1. Associations

2. Ratio measures

3. Difference measures

4. Population attributable risk proportion

5. Summary


1. Associations

2. Ratio measures



5. Summary


Associations

First we start with measures of disease occurrence and frequency

Association now involves the comparison of two measures


Example: Farrlandia associations

Farrlandia population 10,000 people without heart disease Follow population for 5 years 3,000 people smoke 410 of smokers develop heart disease No loss to follow-up or change in smoking status

over time


Example: Farrlandia associations

Risk of heart disease among 3,000 smokers and 7,000 non-smokers, over 5 years


Example: Farrlandia risk

Incidence (risk) Risk of disease among exposed

(smokers)diseased smokers

population at baseline



Incidence (risk) Risk of disease among unexposed

(non-smokers) diseased non-smokers population at baseline



Incidence of heart disease among smokers = 13.7%Incidence of heart disease among non-smokers = 5%

How much larger is 13.7% than 5%?Is the difference between 13.7% and 5% meaningful?


1. Associations

2. Ratio measures



5. Summary


Ratios

A way to quantify the magnitude of difference between two measures of disease


Ratios Risk ratios 95% confidence interval for a risk ratio Example of 95% confidence intervals for a risk ratio Central Limit Theory assumptions and confidence

intervals Rate ratios Odds ratios 95% confidence interval for the odds ratio


Risk ratio

Numerator Conditional risk of disease among exposed

Denominator Conditional risk of disease among unexposed

15Epidemiology Matters – Chapter 6

a b a+b

c d c+d

a+c b+d a+b+c+d


Risk ratio

NumeratorRisk of disease in exposed

DenominatorRisk of disease in unexposed

aa+b

cc+d

=


Disease incidence over time

Non-diseased Diseased

Exposed Unexposed


2 x 2 table


Risk ratio

NumeratorRisk of disease in exposed

DenominatorRisk of disease in unexposed

aa+b

cc+d

=


2 x 2 table

8---10

--------5---10

Risk ratio = = 1.6


2 x 2 table

a---

a+b--------

c---

c+d

Risk ratio =

8---10

--------5---10

Risk ratio =


Risk ratio interpretation

Ratios > 1.0 indicate rate is higher among exposed than unexposed

Ratios = 1.0 indicate no association Ratios < 1.0 indicate rate is lower among

exposed than unexposed


Risk ratio95% confidence interval

Sample, by chance, will often not represent exact disease and exposure experience of population

Confidence intervals help to understand variability in study estimates due to chance in sampling process


Steps: risk ratio95% confidence interval

1. Take natural log of risk ratioln (Risk ratio)

2. Estimate standard error (SE)



3. Estimate upper and lower bounds on log scale 95% confidence interval upper bound

ln(Risk ratio) + 1.96(SE[ln(Risk ratio)]) 95% confidence interval lower bound

ln(Risk ratio) - 1.96(SE[ln(Risk ratio)])



4. Exponentiate upper and lower bounds5. Report and interpret estimate and confidence

intervalSample: In these data, the exposed individuals

had [risk ratio estimate] times the risk of the outcome compared with the unexposed, with a 95% confidence interval for the observed risk ratio ranging from [lower bound] to [upper bound].


Example: risk ratio95% confidence interval

Measure association between family history of Alzheimer’s disease (AD) and incidence of AD among those aged >70

Random sample of 1,000 individuals aged >70, no symptoms of AD

Followed for 20 years Measure symptoms of AD every year No losses to follow-up



a---

a+b--------

c---

c+d

Risk ratio =



1. Take natural log of risk ratioln (Risk ratio) = ln(1.548) =

0.4372. Estimate standard error (SE)




ln(Risk ratio) + 1.96(SE[ln(Risk ratio)])

0.437 + 1.96(0.1796) 95% confidence interval lower bound

ln(Risk ratio) - 1.96(SE[ln(Risk ratio)])

0.437 - 1.96(0.1796)



4. Exponentiate upper and lower bounds

5. Report and interpret estimate and confidence intervalIndividuals >70 in Farrlandia with a family history of AD had 1.55 times the risk of developing AD over 20 years, with a 95% confidence interval for the risk ratio of 1.09 to 2.20.


Central Limit Theory

Validity of confidence interval relies on Central Limit Theory (CLT)

Remember, assumptions of CLT Large sample size Each cell in 2 x 2 ≥ 5


Rate ratio

Risk ratios ideal with little or no loss to follow-up Most studies have substantial loss to follow-up Rate ratio more accurate representation of

incidence when loss to follow-up an issue


Rate ratio


Rate ratio

NumeratorRate of disease in exposed

DenominatorRate of disease in unexposed

=


Rate ratio interpretation

Similar to risk ratio Ratios > 1.0 indicate rate is higher among

exposed than unexposed Ratios = 1.0 indicate no association Ratios < 1.0 indicate rate is lower among

exposed than unexposed


Steps: rate ratio95% confidence interval

1. Take natural log of rate ratioln (Rate ratio)





ln(Rate ratio) + 1.96(SE[ln(Rate ratio)]) 95% confidence interval lower bound

ln(Rate ratio) - 1.96(SE[ln(Rate ratio)])




intervalSample: In these data, the exposed individuals had [rate ratio estimate] times the

rate of the outcome compared with the unexposed, with a 95% confidence interval for the observed rate ratio ranging from [lower bound] to [upper bound].


Odds ratio

Appropriate measure of association for prospective study is risk or rate ratio

If sample individuals with and without disease and retrospectively assess exposure status, appropriate measure of association is odds ratio


Example AResearch question: Is smoking cigarettes during pregnancy a potential cause of offspring attention-deficit hyperactivity disorder (ADHD)?Sample: Recruit 5,000 women during pregnancy who are smokers,

and 5,000 women during pregnancy who are not smokers in Farrlandia

Prospective study Assume no loss to follow-upMeasures: Follow offspring at age 10 and determine which children developed ADHD and which did not


Example A: risk ratioa---

a+b--------

c---

c+d

Risk ratio =


Example A: risk ratio interpretation

From the prospective study, offspring of women who smoked in pregnancy have 1.5 times the risk of developing ADHD over 10 years compared to offspring of women who did not smoke in pregnancy.


Odds ratio

Numerator Odds of disease in exposed

Denominator Odds of disease in unexposed


Example A: odds ratio


Example A: odds ratio

Odds of ADHD among exposed

Odds of ADHD among unexposed

Odds ratio


Example A: odds ratiointerpretation

The odds of developing ADHD in the first 10 years of life among those exposed are 1.53 times the odds of disease in the unexposed.


Example A: odds and risk ratio

Odds ratio = 1.53 Risk ratio = 1.5 Ratios similar when outcome is relatively rare

in the population


Example B: odds ratioResearch question: Is smoking cigarettes during pregnancy a potential cause of offspring attention-deficit hyperactivity disorder (ADHD)?

Sample:

500 10-year-old children in Farrlandia who are seeking care hyperactivity

For each child we find with ADHD, we select two children of the same age from the same physician offices who present for routine well visits (do not have ADHD) – a purposive sample

Case control study

Measures: Mothers respond to questions, including whether they smoked cigarettes while they were pregnant


Example B: odds ratio


Example B: odds ratio

Odds of exposure among those with ADHD:

Odds of exposure among those without ADHD:

Odds ratio in the case control study:


Example B: odds ratiointerpretation

The odds of exposure (mother smoking in pregnancy) among those with ADHD are 1.53 times higher among cases than among controls.


Example A and B: odds ratios

Odds ratio in prospective cohort study = 1.53 Odds ratio in case control study = 1.48


Odds ratio: why we use it (1) Exposure odds ratio and disease odds ratio are mathematically equal!

In the prospective study, we estimated the odds of disease among exposed and odds of disease among unexposed

In the case control study, we estimated the odds of exposure among the diseased and the odds of exposure among the nondiseased.

When we select our cases and controls correctly, we get an unbiased estimate of the exposure odds even though we estimate the disease odds.

This odds ratio is approximately equivalent to the risk ratio when the disease is rare.


Odds ratio: why we use it (2)

“When we select our cases and controls correctly”…– In our example, cases and controls were selected from

the same underlying population base as the sample from the prospective study.

– When cases and controls are selected from the same population base, we can get the same estimate of the association between exposure and disease from the case control study that we would have gotten from a prospective study from the same population base.


Steps: odds ratio95% confidence interval

1. Take natural log of odds ratioln (Odds ratio)





ln(Odds ratio) + 1.96(SE[ln(Odds ratio)]) 95% confidence interval lower bound

ln(Odds ratio) - 1.96(SE[ln(Odds ratio)])




intervalSample: In these data, the exposed individuals

had [odds ratio estimate] times the odds of the outcome compared with the exposed, with a 95% confidence interval for the observed odds ratio ranging from [lower bound] to [upper bound].


Summary: odds ratio

Cannot estimate the risk of disease directly when we sample people based on whether they have the disease or not (case control study)

Can estimate proportion exposed among diseased and non-diseased Estimate odds ratio for exposure Odds ratio for exposure = odds ratio for disease

If disease is rare in population, the odds ratio approximates the risk ratio from a prospective study


1. Associations

2. Ratio measures



5. Summary


Risk difference

Difference between two risks =

Interpretation: Excess risk due to the exposureExample: If the risk of disease is 10 per 100,000 in the unexposed and 15 per 100,000 in the exposed, then 5 per 100,000 cases is associated with the exposure of interest.

Epidemiology Matters – Chapter 6

Example: Nutrition and obesity

Research question: Are nutrition classes in middle school associated with the development of obesity in adolescence?

Sample:

Middle school A, 400 students, receives health education (intervention)

Middle school B, 300 students, in neighboring district, does not receive health nutrition class

Purposive

Measures: Schools collect students’ height and weight yearly for 5 years

65


Example: risk difference


Example: risk difference Incidence proportion (or risk) of obesity among those who had

nutrition class = 0.175 or 17.5% Incidence proportion (or risk) of obesity among those who did not

have nutrition class = 0.33 or 33% Risk difference

Incidence proportion of exposed – incidence proportion of unexposed

0.175 – 0.33= - 0.155 Interpretation: There are approximately 15.5 fewer cases of obesity

during adolescence for every 100 adolescents associated with nutrition class in middle school


Steps: risk difference95% confidence interval




2. Estimate upper and lower bounds 95% confidence interval upper bound

Risk difference + 1.96(SE[Risk difference]) 95% confidence interval lower bound

Risk difference - 1.96(SE[Risk difference])



3. Report and interpret estimate and confidence interval

Sample Positive: In these data, exposure was associated with an excess of [risk difference estimate] cases compared with the unexposed, with a 95% confidence interval for the observed excess cases ranging from [lower bound] to [upper bound].

Sample Negative: In these data, exposure was associated with an [risk difference estimate] fewer cases compared with the unexposed, with a 95% confidence interval for the observed decrease in cases ranging from [lower bound] to [upper bound].


Example: risk difference95% confidence interval





Risk difference + 1.96(SE[Risk difference])

- 0.155 + 1.96(0.02) = -0.1158 95% confidence interval lower bound

Risk difference - 1.96(SE[Risk difference])

- 0.155 - 1.96(0.02) = -0.1942



3. Report and interpret estimate and confidence interval Negative: Middle high nutrition

education is associated with 15.5 fewer cases of obesity per 100 adolescents over five years, with a 95% confidence interval for the observed decrease in cases from 11.6 to 19.4 fewer cases.


Rate difference Difference between two rates

Interpretation: Similar to risk difference; excess rate due to the exposure Example: If the rate of disease is 8 per 100,000 person years in the

exposed and 4 per 100,000 person years in the unexposed, then 4 per 100,000 person-years of exposure is associated with the exposure of interest


Steps: rate difference95% confidence interval

1. Estimate standard error (SE)PY1 = total person time contributed among exposedPY2 = total person time contributed among the unexposed




Rate difference + 1.96(SE[Rate difference]) 95% confidence interval lower bound

Rate difference - 1.96(SE[Rate difference])



3. Report and interpret estimate and confidence interval

Sample Positive: In these data, exposure was associated with an increases of [rate difference estimate] in the rate compared with the unexposed, with a 95% confidence interval for the observed excess rate ranging from [lower bound] to [upper bound].

Sample Negative: In these data, exposure was associated with an decrease of [rate difference estimate] in the rate compared with the unexposed, with a 95% confidence interval for the observed decrease in the rate ranging from [lower bound] to [upper bound].


Risk/rate differencesRisk/rate ratios

When is a ratio measure appropriate versus a difference measure? Why would we use one over the other?


Risk/rate differencesRisk/rate ratios

Difference measures (risk / rate difference) provide a measure of the potential direct public health benefit of intervention.

Ratio measures (risk / rate / odds ratio) provide an intuitive summary of the magnitude of differences in two exposures.


1. Associations

2. Ratio measures



5. Summary


Population attributable risk proportion (PARP)

Population attributable fraction Measure of the proportion of the total disease

burden associated with exposure


Example: PARP

Proportion of people who develop heart disease among smokers and nonsmokers

Risk of heart disease in smokers = 13.7% Risk of heart disease in nonsmokers = 5% PARP would be calculated as:


Example PARP

Interpretation A: 64% of the heart disease in the population of Farrlandia is potentially attributable to smoking.

Interpretation B: If we were to convince all of the smokers to quit, we would reduce the incidence of heart disease by 64%.

PARP is particularly useful measure in public health practice


1. Associations

2. Ratio measures



5. Summary


Seven steps

1. Define the population of interest2. Conceptualize and create measures of exposures and health

indicators3. Take a sample of the population4. Estimate measures of association between exposures and health

indicators of interest5. Rigorously evaluate whether the association observed suggests a

causal association6. Assess the evidence for causes working together7. Assess the extent to which the result matters, is externally valid, to

other populations


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